Ideal gas law- Find the pressure

AI Thread Summary
The discussion centers on confusion regarding the Ideal Gas Law and the treatment of pressure and volume in a worked solution. Participants clarify that the pressure variable is not changing and should remain constant while volume changes. A misunderstanding arises from the notation used in the solution, particularly the use of capital "P" instead of lowercase "p." One participant realizes that the numbers referenced pertain to volume rather than pressure, leading to a correction in their algebra. Ultimately, the conversation emphasizes the importance of consistent notation and careful algebraic manipulation in applying the Ideal Gas Law.
Woopa
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Homework Statement
A container of an ideal gas that is isolated from its surroundings is divided into two parts. One part has double the volume of the other. The pressure in each part is p and the temperature is the same. The partition is removed. What is the pressure in the container now?
Relevant Equations
PV=nRT
Question:
1645529215001.png

Answer:
1645529385444.png

In the third last line of working, I do not understand why the pressure variable is changing? Shouldn't pressure remain constant and only the Volume change?
 
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Woopa said:
In the third last line of working, I do not understand why the pressure variable is changing? Shouldn't pressure remain constant and only the Volume change?
Where do you see anything changing ? Strictly speaking ##p_{\rm\, final} ## is unknown and to be determined.
Then the outcome is ##p_{\rm \, final} = p##

Comment: they use capital ##P## in the solution, which is undesirable: once lower case ##p## , always lower case ##p##

##\ ##
 
The 2 and 3 numbers are for V rather than for p.
 
Lnewqban said:
The 2 and 3 numbers are for V rather than for p.
Do you mean it is a typo/ error in the worked solution?
 
V + 2V = 3V
 
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Lnewqban said:
V + 2V = 3V
Ah yes that make sense I can see now the numbers are actually for V, the way they've written out the equation has confused me.

However I am still arriving at the final answer P=2P. I must be making a mistake in my algebra. I will post my working in a moment
 
1645540153027.jpg


Where is my mistake?
 
##p⋅V/RT+p⋅(2V)/RT=p⋅(V+2V)/RT##
 
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##pV+2pV=p(V+2V)=3pV##

You are saying that it's equal to ##6pV##. That's your error.
 
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